Abstract

An eigenvalue-problem approach of blind deconvolution is developed to retrieve the information of two-dimensional subwavelength variation from far-field irradiance with an embedded-aperture configuration with three detectors. A reference signal has been implemented to determine the scaling issue, and hence it allows the exact order of magnitude of the retrieved signals to be estimated correctly. It is shown that the subwavelength variations of a two-dimensional aperture can be identified with a precision of better than a 1% error ratio.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2005 (2)

2004 (5)

L. S. C. Pingree, M. C. Hersam, M. M. Kern, B. J. Scott, and T. J. Marks, "Spatially-resolved electroluminescence of operating organic light-emitting diodes using conductive atomic force microscopy," Appl. Phys. Lett. 85, 344-346 (2004).
[CrossRef]

K. Nakamoto, C. B. Mooney, and S.-I. Kitamura, "AC mode feedback and gate pulse acquisition methods for scanning near-field optical microscope," Jpn. J. Appl. Phys., Part 1 43, 2686-2689 (2004).
[CrossRef]

B. Niggemann, T. L. DrellIV, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, and F. Entschladen, "Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix," Exp. Cell Res. 298, 178-187 (2004).
[CrossRef] [PubMed]

S. Cooper, "Control and maintenance of mammalian cell size," BMC Cell Biol. 5, 35 (2004); see http://www.biomedcentral.com/1471-2121/5/35.
[CrossRef] [PubMed]

S.-C. Chu and J.-L. Chern, "Characterization of the subwavelength variation signature from far-field irradiance," Opt. Lett. 29, 1045-1047 (2004).
[CrossRef] [PubMed]

2002 (4)

1998 (1)

J.-Y. Ko, M.-C. Ho, J.-L. Chern, R.-R. Hsu, and C.-S. Wang, "Eigenvalue problem approach to the blind source separation: optimization with a reference signal," Phys. Rev. E 58, 4872-4882 (1998).
[CrossRef]

1994 (1)

L. Molgedey and H. G. Schuster, "Separation of a mixture of independent signals using time delayed correlations," Phys. Rev. Lett. 72, 3634-3637 (1994).
[CrossRef] [PubMed]

Biener, G.

Bomzon, Z.

Cao, J. R.

P.-T. Lee, J. R. Cao, S.-J. Choi, Z.-J. Wei, J. D. O'Brien, and P. D. Dapkus, "Operation of photonic crystal membrane lasers above room temperature," Appl. Phys. Lett. 81, 3311-3313 (2002).
[CrossRef]

Chern, J.-L.

Choi, S.-J.

P.-T. Lee, J. R. Cao, S.-J. Choi, Z.-J. Wei, J. D. O'Brien, and P. D. Dapkus, "Operation of photonic crystal membrane lasers above room temperature," Appl. Phys. Lett. 81, 3311-3313 (2002).
[CrossRef]

Chu, S.-C.

Cichocki, A.

A. Cichocki and R. Unbehauen, Neural Networks for Optimization and Signal Processing (Wiley, 1995).

Cooper, S.

S. Cooper, "Control and maintenance of mammalian cell size," BMC Cell Biol. 5, 35 (2004); see http://www.biomedcentral.com/1471-2121/5/35.
[CrossRef] [PubMed]

Dapkus, P. D.

P.-T. Lee, J. R. Cao, S.-J. Choi, Z.-J. Wei, J. D. O'Brien, and P. D. Dapkus, "Operation of photonic crystal membrane lasers above room temperature," Appl. Phys. Lett. 81, 3311-3313 (2002).
[CrossRef]

Drell, T. L.

B. Niggemann, T. L. DrellIV, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, and F. Entschladen, "Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix," Exp. Cell Res. 298, 178-187 (2004).
[CrossRef] [PubMed]

Entschladen, F.

B. Niggemann, T. L. DrellIV, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, and F. Entschladen, "Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix," Exp. Cell Res. 298, 178-187 (2004).
[CrossRef] [PubMed]

Hasman, E.

Hersam, M. C.

L. S. C. Pingree, M. C. Hersam, M. M. Kern, B. J. Scott, and T. J. Marks, "Spatially-resolved electroluminescence of operating organic light-emitting diodes using conductive atomic force microscopy," Appl. Phys. Lett. 85, 344-346 (2004).
[CrossRef]

Ho, M.-C.

J.-Y. Ko, M.-C. Ho, J.-L. Chern, R.-R. Hsu, and C.-S. Wang, "Eigenvalue problem approach to the blind source separation: optimization with a reference signal," Phys. Rev. E 58, 4872-4882 (1998).
[CrossRef]

Hsu, R.-R.

J.-Y. Ko, M.-C. Ho, J.-L. Chern, R.-R. Hsu, and C.-S. Wang, "Eigenvalue problem approach to the blind source separation: optimization with a reference signal," Phys. Rev. E 58, 4872-4882 (1998).
[CrossRef]

Joseph, J.

B. Niggemann, T. L. DrellIV, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, and F. Entschladen, "Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix," Exp. Cell Res. 298, 178-187 (2004).
[CrossRef] [PubMed]

Kern, M. M.

L. S. C. Pingree, M. C. Hersam, M. M. Kern, B. J. Scott, and T. J. Marks, "Spatially-resolved electroluminescence of operating organic light-emitting diodes using conductive atomic force microscopy," Appl. Phys. Lett. 85, 344-346 (2004).
[CrossRef]

Kitamura, S.-I.

K. Nakamoto, C. B. Mooney, and S.-I. Kitamura, "AC mode feedback and gate pulse acquisition methods for scanning near-field optical microscope," Jpn. J. Appl. Phys., Part 1 43, 2686-2689 (2004).
[CrossRef]

Kleiner, V.

Ko, J.-Y.

J.-Y. Ko, M.-C. Ho, J.-L. Chern, R.-R. Hsu, and C.-S. Wang, "Eigenvalue problem approach to the blind source separation: optimization with a reference signal," Phys. Rev. E 58, 4872-4882 (1998).
[CrossRef]

Lang, K.

B. Niggemann, T. L. DrellIV, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, and F. Entschladen, "Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix," Exp. Cell Res. 298, 178-187 (2004).
[CrossRef] [PubMed]

Lee, P.-T.

P.-T. Lee, J. R. Cao, S.-J. Choi, Z.-J. Wei, J. D. O'Brien, and P. D. Dapkus, "Operation of photonic crystal membrane lasers above room temperature," Appl. Phys. Lett. 81, 3311-3313 (2002).
[CrossRef]

Li, C.-C.

Marks, T. J.

L. S. C. Pingree, M. C. Hersam, M. M. Kern, B. J. Scott, and T. J. Marks, "Spatially-resolved electroluminescence of operating organic light-emitting diodes using conductive atomic force microscopy," Appl. Phys. Lett. 85, 344-346 (2004).
[CrossRef]

Molgedey, L.

L. Molgedey and H. G. Schuster, "Separation of a mixture of independent signals using time delayed correlations," Phys. Rev. Lett. 72, 3634-3637 (1994).
[CrossRef] [PubMed]

Mooney, C. B.

K. Nakamoto, C. B. Mooney, and S.-I. Kitamura, "AC mode feedback and gate pulse acquisition methods for scanning near-field optical microscope," Jpn. J. Appl. Phys., Part 1 43, 2686-2689 (2004).
[CrossRef]

Nakamoto, K.

K. Nakamoto, C. B. Mooney, and S.-I. Kitamura, "AC mode feedback and gate pulse acquisition methods for scanning near-field optical microscope," Jpn. J. Appl. Phys., Part 1 43, 2686-2689 (2004).
[CrossRef]

Niggemann, B.

B. Niggemann, T. L. DrellIV, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, and F. Entschladen, "Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix," Exp. Cell Res. 298, 178-187 (2004).
[CrossRef] [PubMed]

O'Brien, J. D.

P.-T. Lee, J. R. Cao, S.-J. Choi, Z.-J. Wei, J. D. O'Brien, and P. D. Dapkus, "Operation of photonic crystal membrane lasers above room temperature," Appl. Phys. Lett. 81, 3311-3313 (2002).
[CrossRef]

Pingree, L. S. C.

L. S. C. Pingree, M. C. Hersam, M. M. Kern, B. J. Scott, and T. J. Marks, "Spatially-resolved electroluminescence of operating organic light-emitting diodes using conductive atomic force microscopy," Appl. Phys. Lett. 85, 344-346 (2004).
[CrossRef]

Righini, M.

Schuster, H. G.

L. Molgedey and H. G. Schuster, "Separation of a mixture of independent signals using time delayed correlations," Phys. Rev. Lett. 72, 3634-3637 (1994).
[CrossRef] [PubMed]

Scott, B. J.

L. S. C. Pingree, M. C. Hersam, M. M. Kern, B. J. Scott, and T. J. Marks, "Spatially-resolved electroluminescence of operating organic light-emitting diodes using conductive atomic force microscopy," Appl. Phys. Lett. 85, 344-346 (2004).
[CrossRef]

Selci, S.

Tseng, S.-H.

Unbehauen, R.

A. Cichocki and R. Unbehauen, Neural Networks for Optimization and Signal Processing (Wiley, 1995).

Wang, C.-S.

J.-Y. Ko, M.-C. Ho, J.-L. Chern, R.-R. Hsu, and C.-S. Wang, "Eigenvalue problem approach to the blind source separation: optimization with a reference signal," Phys. Rev. E 58, 4872-4882 (1998).
[CrossRef]

Wei, Z.-J.

P.-T. Lee, J. R. Cao, S.-J. Choi, Z.-J. Wei, J. D. O'Brien, and P. D. Dapkus, "Operation of photonic crystal membrane lasers above room temperature," Appl. Phys. Lett. 81, 3311-3313 (2002).
[CrossRef]

Weidt, C.

B. Niggemann, T. L. DrellIV, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, and F. Entschladen, "Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix," Exp. Cell Res. 298, 178-187 (2004).
[CrossRef] [PubMed]

Zaenker, K. S.

B. Niggemann, T. L. DrellIV, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, and F. Entschladen, "Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix," Exp. Cell Res. 298, 178-187 (2004).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

P.-T. Lee, J. R. Cao, S.-J. Choi, Z.-J. Wei, J. D. O'Brien, and P. D. Dapkus, "Operation of photonic crystal membrane lasers above room temperature," Appl. Phys. Lett. 81, 3311-3313 (2002).
[CrossRef]

L. S. C. Pingree, M. C. Hersam, M. M. Kern, B. J. Scott, and T. J. Marks, "Spatially-resolved electroluminescence of operating organic light-emitting diodes using conductive atomic force microscopy," Appl. Phys. Lett. 85, 344-346 (2004).
[CrossRef]

BMC Cell Biol. (1)

S. Cooper, "Control and maintenance of mammalian cell size," BMC Cell Biol. 5, 35 (2004); see http://www.biomedcentral.com/1471-2121/5/35.
[CrossRef] [PubMed]

Exp. Cell Res. (1)

B. Niggemann, T. L. DrellIV, J. Joseph, C. Weidt, K. Lang, K. S. Zaenker, and F. Entschladen, "Tumor cell locomotion: differential dynamics of spontaneous and induced migration in a 3D collagen matrix," Exp. Cell Res. 298, 178-187 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (2)

Jpn. J. Appl. Phys., Part 1 (1)

K. Nakamoto, C. B. Mooney, and S.-I. Kitamura, "AC mode feedback and gate pulse acquisition methods for scanning near-field optical microscope," Jpn. J. Appl. Phys., Part 1 43, 2686-2689 (2004).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. E (1)

J.-Y. Ko, M.-C. Ho, J.-L. Chern, R.-R. Hsu, and C.-S. Wang, "Eigenvalue problem approach to the blind source separation: optimization with a reference signal," Phys. Rev. E 58, 4872-4882 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

L. Molgedey and H. G. Schuster, "Separation of a mixture of independent signals using time delayed correlations," Phys. Rev. Lett. 72, 3634-3637 (1994).
[CrossRef] [PubMed]

Other (1)

A. Cichocki and R. Unbehauen, Neural Networks for Optimization and Signal Processing (Wiley, 1995).

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Figures (4)

Fig. 1
Fig. 1

Schematic diagrams of (a) a two-detector configuration and (b) the relative positions of the two detectors.

Fig. 2
Fig. 2

Simulation and comparison of a two-detector configuration where Δ a and Δ b are the aperture-width variations set in advance and Δ a and Δ b are the corresponding quantities after retrieving (see text).

Fig. 3
Fig. 3

Schematic diagrams of (a) an embedded-aperture three-detector interferometer and (b) the relative positions of the detectors. (c) Schematic diagram of the sizes of the two apertures.

Fig. 4
Fig. 4

(a) Inverse mean error of the retrieving embedded-aperture variation versus the time delay, τ. (b) The error and error percentage between setting and retrieving aperture-width variations Δ a and Δ a . (c) The error and error percentage between setting and retrieving aperture-width variations Δ b and Δ b .

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

[ Δ P 1 Δ P 2 ] = [ P 1 a P 1 b P 2 a P 2 b ] [ Δ a Δ b ] ,
[ Δ P 1 Δ P 2 ] = [ P 1 a α 1 P 1 b α 2 P 2 a α 1 P 2 a α 2 ] [ α 1 Δ a α 2 Δ b ] ,
[ Δ P 1 Δ P 2 Δ P 3 ] = [ P 1 a α 1 P 1 b α 2 P 1 d α 3 P 2 a α 1 P 2 b α 2 P 2 d α 3 P 3 a α 1 P 3 b α 2 P 3 d α 3 ] [ α 1 Δ a α 2 Δ b α 3 Δ d ] .
P 3 b = 16 λ 2 k Z P a ( a , d , W 2 ) Si ( k b W Z ) ,
P 3 a = 16 λ 2 k Z P b ( b , W 2 ) { Si ( k a W Z ) + Si [ k ( a + d ) W 2 Z ] Si [ k ( a d ) W 2 Z ] } ,
P a ( a , d , W 2 ) = 0 W 2 [ sin ( k x a Z ) + sin ( k x d Z ) ] 2 ( π x λ Z ) 2 d x ,
P b ( b , W 2 ) = 0 W 2 sin 2 ( k y b Z ) ( π y λ Z ) 2 d y
inverse mean error = 1 Δ d ( t ) Δ d ( t ) .

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